Pricing general insurance with constraints

Book English OPEN
Emms, P. (2006)
  • Publisher: Faculty of Actuarial Science & Insurance, City University London
  • Subject: HG

Deterministic control theory is used to find the optimal premium strategy for an insurer in order to maximise a given objective. The optimal strategy can be loss-leading depending on the model parameters, which may result in negative premium values. In such circumstances, it is optimal to capture as much of the market as possible before making a profit towards the end of the time horizon. In reality, the amount by which an insurer can lower premiums is constrained by borrowing restrictions and the risk inherent in building up a large exposure. Consequently, the effect of constraining the pricing problem is analysed with two forms of constraint: a bounded premium and a solvency requirement. If a lower bound is placed on the premium then an analytical solution can be found, which is not necessarily a smooth function of time. The optimal premium strategy is described in qualitative terms, without recourse to specifying particular parameter values, by considering the value of the terminal optimal premium. Solvency constraints lead to an optimisation problem which is coupled to the state equations and so there is no analytical solution. Numerical results are presented for a subset of the parameter space using control parameterisation, which turns the optimisation problem into a nonlinear programming problem.
  • References (14)
    14 references, page 1 of 2

    Daykin, C. D., Pentika¨inen, T., & Pesonen, M. 1994. Practical Risk Theory for Actuaries. Chapman and Hall.

    Emms, P. 2006. Dynamic pricing of general insurance in a competitive market. (under review) Cass Business School, City University, London.

    Emms, P., & Haberman, S. 2005. Pricing general insurance using optimal control theory. Astin Bulletin, 35(2), 427-453.

    Fleming, W., & Rishel, R. 1975. Deterministic and Stochastic Optimal Control. New York: Springer Verlag.

    Fleming, W. H., & Soner, H. M. 1993. Controlled Markov Processes and Viscosity Solutions. Springer-Verlag.

    Gerber, H. U., & Pafumi, G. 1998. Utility Functions: From Risk Theory to Finance. North American Actuarial Journal, 2(3), 74-100.

    Lilien, G. L., & Kotler, P. 1983. Marketing Decision Making. Harper & Row.

    Rolski, T., Schmidli, H., Schmidt, V., & Teugels, J. 1999. Stochastic Processes for Insurance and Finance. Wiley.

    Sethi, S. P., & Thompson, G. L. 2000. Optimal Control Theory. 2nd edn. Kluwer Academic Publishers.

    Spellucci, P. 1998a. donlp2: general differentiable nonlinear programming using dense linear algebra. Available at http://www.netlib.org/opt/.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    72
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    City Research Online - IRUS-UK 0 72
Share - Bookmark